I've always thought it's foolish to leave a current partner for someone new.
If your current relationship has problems that cannot be overcome, that is a good reason to leave. But simply leaving because someone else has turned your head is rash - other people will get hurt, and there is every chance you will regret it down the line. Just look at how many men beg for their wives' forgiveness after they leave for another woman and it goes sour.
Examine your marriage. Talk to your husband, get counselling if there's a chance of salvaging what you once had. If it really is the end, then deal with that first and keep your family at the forefront of your mind.
Once the divorce is finalised, the house sold, your new home set up, and your children have come to terms with it all, then and only then is it ok to start to pursue a new relationship - that's if you're serious about not hurting anyone.
It's irrelevant if you think your husband is cold and uncaring. It's irrelevant if you're in love with someone else. If you use those things as excuses, you will let yourself down.
Have a look at the "do they ever come back" thread that's currently active, and imagine it all from your husband's perspective. I know it's hard when you're blinded by intense feelings, but please try to do the right thing.